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As described in the papers, the portfolio value function for this curve matches the Black-Scholes valuation of a covered call (with strike price of 1).
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To get the liquidity fingerprint, first, take the formula for y a function of the square root of price:
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Take the derivative:
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Express it in terms of log price rather than square root of price to get the liquidity fingerprint:
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This turns out to be the normal curve with v*sqrt(t) as the standard deviation, scaled a bit:
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